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Evaluate following double integral value taking 4 segment for both x and y direction use Simpson rule ∫(2)_(4)∫(x)_(3x^2) ((3x^2)+y) dy dx

obtain second order derivative y'' using Taylor series Expansion using 4 point

solve the problem d^2T/dx^2 = dT/dt when

T(0,t)=200,T(1,t)=200,T(x,0)=0 using boundary and initial conditions above with dalta x =0.2 solve the parabolic equation for dalta t=0.04 and dalta t=0.015 time step. compare there two results.

T(0,t)=200,T(1,t)=200,T(x,0)=0 using boundary and initial conditions above with dalta x =0.2 solve the parabolic equation for dalta t=0.04 and dalta t=0.015 time step. compare there two results.

A new design of nitrogen charged accumulator, for use in a hydraulic circuit, is being factory tested for certification purposes.(http://www.accumulators.co.uk/). The following data has been collected by a technician:

o Gas volume: V = 0.8 m3

o Gas pressure: p = 160 kPa

o Compression index: n = 1.4

o Pressure/volume relationship: pV ⁿ = C

o Work done =

i. Evaluate C.

ii. Calculate the work done in compressing the nitrogen from 0.8 m3 to 0.6 m3 using:

o integral calculus

o Gas volume: V = 0.8 m3

o Gas pressure: p = 160 kPa

o Compression index: n = 1.4

o Pressure/volume relationship: pV ⁿ = C

o Work done =

i. Evaluate C.

ii. Calculate the work done in compressing the nitrogen from 0.8 m3 to 0.6 m3 using:

o integral calculus

A new design of nitrogen charged accumulator, for use in a hydraulic circuit, is being factory tested for certification purposes.(http://www.accumulators.co.uk/). The following data has been collected by a technician:

o Gas volume: V = 0.8 m3

o Gas pressure: p = 160 kPa

o Compression index: n = 1.4

o Pressure/volume relationship: pV ⁿ = C

o Work done =

i. Evaluate C.

ii. Calculate the work done in compressing the nitrogen from 0.8 m3 to 0.6 m3 using

=mid-oridnate rule

o Gas volume: V = 0.8 m3

o Gas pressure: p = 160 kPa

o Compression index: n = 1.4

o Pressure/volume relationship: pV ⁿ = C

o Work done =

i. Evaluate C.

ii. Calculate the work done in compressing the nitrogen from 0.8 m3 to 0.6 m3 using

=mid-oridnate rule

A new design of nitrogen charged accumulator, for use in a hydraulic circuit, is being factory tested for certification purposes.(http://www.accumulators.co.uk/). The following data has been collected by a technician:

o Gas volume: V = 0.8 m3

o Gas pressure: p = 160 kPa

o Compression index: n = 1.4

o Pressure/volume relationship: pV ⁿ = C

o Work done =

i. Evaluate C.

ii. Calculate the work done in compressing the nitrogen from 0.8 m3 to 0.6 m3 using:

o integral calculus

o Simpson’s rule

o the mid-ordinate rule.

o Gas volume: V = 0.8 m3

o Gas pressure: p = 160 kPa

o Compression index: n = 1.4

o Pressure/volume relationship: pV ⁿ = C

o Work done =

i. Evaluate C.

ii. Calculate the work done in compressing the nitrogen from 0.8 m3 to 0.6 m3 using:

o integral calculus

o Simpson’s rule

o the mid-ordinate rule.

A new design of nitrogen charged accumulator, for use in a hydraulic circuit, is being factory tested for certification purposes.(http://www.accumulators.co.uk/). The following data has been collected by a technician:

o Gas volume: V = 0.8 m3

o Gas pressure: p = 160 kPa

o Compression index: n = 1.4

o Pressure/volume relationship: pV ⁿ = C

o Work done =

i. Evaluate C.

ii. Calculate the work done in compressing the nitrogen from 0.8 m3 to 0.6 m3 using:

o integral calculus

o Simpson’s rule

o the mid-ordinate rule.

iii. Comment on the accuracy of the two numerical methods.

o Gas volume: V = 0.8 m3

o Gas pressure: p = 160 kPa

o Compression index: n = 1.4

o Pressure/volume relationship: pV ⁿ = C

o Work done =

i. Evaluate C.

ii. Calculate the work done in compressing the nitrogen from 0.8 m3 to 0.6 m3 using:

o integral calculus

o Simpson’s rule

o the mid-ordinate rule.

iii. Comment on the accuracy of the two numerical methods.

A new design of nitrogen charged accumulator, for use in a hydraulic circuit, is being factory tested for certification purposes.(http://www.accumulators.co.uk/). The following data has been collected by a technician:

o Gas volume: V = 0.8 m3

o Gas pressure: p = 160 kPa

o Compression index: n = 1.4

o Pressure/volume relationship: pV ⁿ = C

o Work done =

i. Evaluate C.

ii. Calculate the work done in compressing the nitrogen from 0.8 m3 to 0.6 m3 using:

o integral calculus

o Simpson’s rule

o Gas volume: V = 0.8 m3

o Gas pressure: p = 160 kPa

o Compression index: n = 1.4

o Pressure/volume relationship: pV ⁿ = C

o Work done =

i. Evaluate C.

ii. Calculate the work done in compressing the nitrogen from 0.8 m3 to 0.6 m3 using:

o integral calculus

o Simpson’s rule

The following table of values of f(x) is given:

x →0.25 0.30 0.35

f(x)→1.25 1.90 1.68

Compute f'(x) at x=0.30 using an O(h²) formula.

x →0.25 0.30 0.35

f(x)→1.25 1.90 1.68

Compute f'(x) at x=0.30 using an O(h²) formula.

6 0 0.5| x' =1

0.5 2 - 1 | x'' = - 1

3 1 0 | x''' =2

Solve the system by LU decomposition method

0.5 2 - 1 | x'' = - 1

3 1 0 | x''' =2

Solve the system by LU decomposition method